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Theorem nfdm 5249
 Description: Bound-variable hypothesis builder for domain. (Contributed by NM, 30-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrn.1
Assertion
Ref Expression
nfdm

Proof of Theorem nfdm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dm 5014 . 2
2 nfcv 2619 . . . . 5
3 nfrn.1 . . . . 5
4 nfcv 2619 . . . . 5
52, 3, 4nfbr 4496 . . . 4
65nfex 1948 . . 3
76nfab 2623 . 2
81, 7nfcxfr 2617 1
 Colors of variables: wff setvar class Syntax hints:  E.wex 1612  {cab 2442  F/_wnfc 2605   class class class wbr 4452  domcdm 5004 This theorem is referenced by:  nfrn  5250  dmiin  5251  nffn  5682  funimass4f  27474  itgsinexplem1  31752  fourierdlem16  31905  fourierdlem21  31910  fourierdlem22  31911  fourierdlem68  31957  fourierdlem80  31969  fourierdlem103  31992  fourierdlem104  31993  nfdfat  32215  bnj1398  34090  bnj1491  34113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-dm 5014
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